/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

/**

@defgroup datas Data Structures

This group describes the several graph structures implemented in LEMON.

*/

/**

@defgroup graphs Graph Structures

@ingroup datas

\brief Graph structures implemented in LEMON.

The implementation of combinatorial algorithms heavily relies on 

efficient graph implementations. LEMON offers data structures which are 

planned to be easily used in an experimental phase of implementation studies, 

and thereafter the program code can be made efficient by small modifications. 

The most efficient implementation of diverse applications require the

usage of different physical graph implementations. These differences

appear in the size of graph we require to handle, memory or time usage

limitations or in the set of operations through which the graph can be

accessed.  LEMON provides several physical graph structures to meet

the diverging requirements of the possible users.  In order to save on

running time or on memory usage, some structures may fail to provide

some graph features like edge or node deletion.

Alteration of standard containers need a very limited number of 

operations, these together satisfy the everyday requirements. 

In the case of graph structures, different operations are needed which do 

not alter the physical graph, but gives another view. If some nodes or 

edges have to be hidden or the reverse oriented graph have to be used, then 

this is the case. It also may happen that in a flow implementation 

the residual graph can be accessed by another algorithm, or a node-set 

is to be shrunk for another algorithm. 

LEMON also provides a variety of graphs for these requirements called 

\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only 

in conjunction with other graph representation. 

You are free to use the graph structure that fit your requirements

the best, most graph algorithms and auxiliary data structures can be used

with any graph structures. 

*/

/**

@defgroup semi_adaptors Semi-Adaptors Classes for Graphs

@ingroup graphs

\brief Graph types between real graphs and graph adaptors.

Graph types between real graphs and graph adaptors. These classes wrap

graphs to give new functionality as the adaptors do it. On the other

hand they are not light-weight structures as the adaptors.

*/

/**

@defgroup maps Maps 

@ingroup datas

\brief Some special purpose map to make life easier.

LEMON provides several special maps that e.g. combine

new maps from existing ones.

*/

/**

@defgroup graph_maps Graph Maps 

@ingroup maps

\brief Special Graph-Related Maps.

These maps are specifically designed to assign values to the nodes and edges of

graphs.

*/

/**

\defgroup map_adaptors Map Adaptors

\ingroup maps

\brief Tools to create new maps from existing ones

Map adaptors are used to create "implicit" maps from other maps.

Most of them are \ref lemon::concepts::ReadMap "ReadMap"s. They can

make arithmetic operations between one or two maps (negation, scaling,

addition, multiplication etc.) or e.g. convert a map to another one

of different Value type.

The typical usage of this classes is the passing implicit maps to

algorithms.  If a function type algorithm is called then the function

type map adaptors can be used comfortable. For example let's see the

usage of map adaptors with the \c graphToEps() function:

\code

  Color nodeColor(int deg) {

    if (deg >= 2) {

      return Color(0.5, 0.0, 0.5);

    } else if (deg == 1) {

      return Color(1.0, 0.5, 1.0);

    } else {

      return Color(0.0, 0.0, 0.0);

    }

  }

  Graph::NodeMap<int> degree_map(graph);

  graphToEps(graph, "graph.eps")

    .coords(coords).scaleToA4().undirected()

    .nodeColors(composeMap(functorMap(nodeColor), degree_map)) 

    .run();

\endcode 

The \c functorMap() function makes an \c int to \c Color map from the

\e nodeColor() function. The \c composeMap() compose the \e degree_map

and the previous created map. The composed map is proper function to

get color of each node.

The usage with class type algorithms is little bit harder. In this

case the function type map adaptors can not be used, because the

function map adaptors give back temporarly objects.

\code

  Graph graph;

  typedef Graph::EdgeMap<double> DoubleEdgeMap;

  DoubleEdgeMap length(graph);

  DoubleEdgeMap speed(graph);

  typedef DivMap<DoubleEdgeMap, DoubleEdgeMap> TimeMap;

  TimeMap time(length, speed);

  Dijkstra<Graph, TimeMap> dijkstra(graph, time);

  dijkstra.run(source, target);

\endcode

We have a length map and a maximum speed map on a graph. The minimum

time to pass the edge can be calculated as the division of the two

maps which can be done implicitly with the \c DivMap template

class. We use the implicit minimum time map as the length map of the

\c Dijkstra algorithm.

*/

/**

@defgroup matrices Matrices 

@ingroup datas

\brief Two dimensional data storages.

Two dimensional data storages.

*/

/**

@defgroup paths Path Structures

@ingroup datas

\brief Path structures implemented in LEMON.

LEMON provides flexible data structures

to work with paths.

All of them have similar interfaces, and it can be copied easily with

assignment operator and copy constructor. This make it easy and

efficient to have e.g. the Dijkstra algorithm to store its result in

any kind of path structure.

\sa lemon::concepts::Path

*/

/**

@defgroup auxdat Auxiliary Data Structures

@ingroup datas

\brief Some data structures implemented in LEMON.

This group describes the data structures implemented in LEMON in

order to make it easier to implement combinatorial algorithms.

*/

/**

@defgroup algs Algorithms

\brief This group describes the several algorithms

implemented in LEMON.

This group describes the several algorithms

implemented in LEMON.

*/

/**

@defgroup search Graph Search

@ingroup algs

\brief This group contains the common graph

search algorithms.

This group contains the common graph

search algorithms like Bfs and Dfs.

*/

/**

@defgroup shortest_path Shortest Path algorithms

@ingroup algs

\brief This group describes the algorithms

for finding shortest paths.

This group describes the algorithms for finding shortest paths in

graphs.

*/

/** 

@defgroup max_flow Maximum Flow algorithms 

@ingroup algs 

\brief This group describes the algorithms for finding maximum flows.

This group describes the algorithms for finding maximum flows and

feasible circulations.

The maximum flow problem is to find a flow between a single-source and

single-target that is maximum. Formally, there is \f$G=(V,A)\f$

directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity

function and given \f$s, t \in V\f$ source and target node. The

maximum flow is the solution of the next optimization problem:

\f[ 0 \le f_a \le c_a \f]

\f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} \quad u \in V \setminus \{s,t\}\f]

\f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]

The lemon contains several algorithms for solve maximum flow problems:

- \ref lemon::EdmondsKarp "Edmonds-Karp" 

- \ref lemon::Preflow "Goldberg's Preflow algorithm"

- \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic tree"

- \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"

In most cases the \ref lemon::Preflow "preflow" algorithm provides the

fastest method to compute the maximum flow. All impelementations

provides functions for query the minimum cut, which is the dual linear

programming probelm of the maximum flow.

*/

/**

@defgroup min_cost_flow Minimum Cost Flow algorithms

@ingroup algs

\brief This group describes the algorithms

for finding minimum cost flows and circulations.

This group describes the algorithms for finding minimum cost flows and

circulations.  

*/

/**

@defgroup min_cut Minimum Cut algorithms 

@ingroup algs 

\brief This group describes the algorithms for finding minimum cut in

graphs.

This group describes the algorithms for finding minimum cut in graphs.

The minimum cut problem is to find a non-empty and non-complete

\f$X\f$ subset of the vertices with minimum overall capacity on

outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an

\f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

cut is the solution of the next optimization problem:

\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}\sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]

The lemon contains several algorithms related to minimum cut problems:

- \ref lemon::HaoOrlin "Hao-Orlin algorithm" for calculate minimum cut

  in directed graphs  

- \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for

  calculate minimum cut in undirected graphs

- \ref lemon::GomoryHuTree "Gomory-Hu tree computation" for calculate all

  pairs minimum cut in undirected graphs

If you want to find minimum cut just between two distinict nodes,

please see the \ref max_flow "Maximum Flow page".

*/

/**

@defgroup graph_prop Connectivity and other graph properties

@ingroup algs

\brief This group describes the algorithms

for discover the graph properties

This group describes the algorithms for discover the graph properties

like connectivity, bipartiteness, euler property, simplicity, etc...

\image html edge_biconnected_components.png

\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth

*/

/**

@defgroup planar Planarity embedding and drawing

@ingroup algs

\brief This group contains algorithms for planarity embedding and drawing

This group contains algorithms for planarity checking, embedding and drawing.

\image html planar.png

\image latex planar.eps "Plane graph" width=\textwidth

*/

/**

@defgroup matching Matching algorithms 

@ingroup algs

\brief This group describes the algorithms

for find matchings in graphs and bipartite graphs.

This group provides some algorithm objects and function to calculate

matchings in graphs and bipartite graphs. The general matching problem is

finding a subset of the edges which does not shares common endpoints.

There are several different algorithms for calculate matchings in

graphs.  The matching problems in bipartite graphs are generally

easier than in general graphs. The goal of the matching optimization

can be the finding maximum cardinality, maximum weight or minimum cost

matching. The search can be constrained to find perfect or

maximum cardinality matching.

Lemon contains the next algorithms:

- \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp 

  augmenting path algorithm for calculate maximum cardinality matching in 

  bipartite graphs

- \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel 

  algorithm for calculate maximum cardinality matching in bipartite graphs 

- \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching" 

  Successive shortest path algorithm for calculate maximum weighted matching 

  and maximum weighted bipartite matching in bipartite graph

- \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching" 

  Successive shortest path algorithm for calculate minimum cost maximum 

  matching in bipartite graph

- \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm

  for calculate maximum cardinality matching in general graph

- \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom

  shrinking algorithm for calculate maximum weighted matching in general

  graph

- \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching"

  Edmond's blossom shrinking algorithm for calculate maximum weighted

  perfect matching in general graph

\image html bipartite_matching.png

\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth

*/

/**

@defgroup spantree Minimum Spanning Tree algorithms

@ingroup algs

\brief This group contains the algorithms for finding a minimum cost spanning

tree in a graph

This group contains the algorithms for finding a minimum cost spanning

tree in a graph

*/

/**

@defgroup auxalg Auxiliary algorithms

@ingroup algs

\brief Some algorithms implemented in LEMON.

This group describes the algorithms in LEMON in order to make 

it easier to implement complex algorithms.

*/

/**

@defgroup approx Approximation algorithms

\brief Approximation algorithms

Approximation and heuristic algorithms

*/

/**

@defgroup gen_opt_group General Optimization Tools

\brief This group describes some general optimization frameworks

implemented in LEMON.

This group describes some general optimization frameworks

implemented in LEMON.

*/

/**

@defgroup lp_group Lp and Mip solvers

@ingroup gen_opt_group

\brief Lp and Mip solver interfaces for LEMON.

This group describes Lp and Mip solver interfaces for LEMON. The

various LP solvers could be used in the same manner with this

interface.

*/

/** 

@defgroup lp_utils Tools for Lp and Mip solvers 

@ingroup lp_group

\brief This group adds some helper tools to the Lp and Mip solvers

implemented in LEMON.

This group adds some helper tools to general optimization framework

implemented in LEMON.

*/

/**

@defgroup metah Metaheuristics

@ingroup gen_opt_group

\brief Metaheuristics for LEMON library.

This group contains some metaheuristic optimization tools.

*/

/**

@defgroup utils Tools and Utilities 

\brief Tools and Utilities for Programming in LEMON

Tools and Utilities for Programming in LEMON

*/

/**

@defgroup gutils Basic Graph Utilities

@ingroup utils

\brief This group describes some simple basic graph utilities.

This group describes some simple basic graph utilities.

*/

/**

@defgroup misc Miscellaneous Tools

@ingroup utils

Here you can find several useful tools for development,

debugging and testing.

*/

/**

@defgroup timecount Time measuring and Counting

@ingroup misc

Here you can find simple tools for measuring the performance

of algorithms.

*/

/**

@defgroup graphbits Tools for Graph Implementation

@ingroup utils

\brief Tools to Make It Easier to Make Graphs.

This group describes the tools that makes it easier to make graphs and

the maps that dynamically update with the graph changes.

*/

/**

@defgroup exceptions Exceptions

@ingroup utils

This group contains the exceptions thrown by LEMON library

*/

/**

@defgroup io_group Input-Output

\brief Several Graph Input-Output methods

Here you can find tools for importing and exporting graphs 

and graph related data. Now it supports the LEMON format, the

\c DIMACS format and the encapsulated postscript format.

*/

/**

@defgroup lemon_io Lemon Input-Output

@ingroup io_group

\brief Reading and writing LEMON format

Methods for reading and writing LEMON format. More about this

format you can find on the \ref graph-io-page "Graph Input-Output"

tutorial pages.

*/

/**

@defgroup section_io Section readers and writers

@ingroup lemon_io

\brief Section readers and writers for lemon Input-Output.

Here you can find which section readers and writers can attach to

the LemonReader and LemonWriter.

*/

/**

@defgroup item_io Item Readers and Writers

@ingroup lemon_io

\brief Item readers and writers for lemon Input-Output.

The Input-Output classes can handle more data type by example

as map or attribute value. Each of these should be written and

read some way. The module make possible to do this.  

*/

/**

@defgroup eps_io Postscript exporting

@ingroup io_group

\brief General \c EPS drawer and graph exporter

This group contains general \c EPS drawing methods and special

graph exporting tools. 

*/

/**

@defgroup concept Concepts

\brief Skeleton classes and concept checking classes

This group describes the data/algorithm skeletons and concept checking

classes implemented in LEMON.

The purpose of the classes in this group is fourfold.

- These classes contain the documentations of the concepts. In order

  to avoid document multiplications, an implementation of a concept

  simply refers to the corresponding concept class.

- These classes declare every functions, <tt>typedef</tt>s etc. an

  implementation of the concepts should provide, however completely

  without implementations and real data structures behind the

  interface. On the other hand they should provide nothing else. All

  the algorithms working on a data structure meeting a certain concept

  should compile with these classes. (Though it will not run properly,

  of course.) In this way it is easily to check if an algorithm

  doesn't use any extra feature of a certain implementation.

- The concept descriptor classes also provide a <em>checker class</em>

  that makes it possible check whether a certain implementation of a

  concept indeed provides all the required features.

- Finally, They can serve as a skeleton of a new implementation of a concept.

*/

/**

@defgroup graph_concepts Graph Structure Concepts

@ingroup concept

\brief Skeleton and concept checking classes for graph structures

This group contains the skeletons and concept checking classes of LEMON's

graph structures and helper classes used to implement these.

*/

/* --- Unused group

@defgroup experimental Experimental Structures and Algorithms

This group contains some Experimental structures and algorithms.

The stuff here is subject to change.

*/

/**

\anchor demoprograms

@defgroup demos Demo programs

Some demo programs are listed here. Their full source codes can be found in

the \c demo subdirectory of the source tree.

The standard compilation procedure (<tt>./configure;make</tt>) will compile

them, as well. 

*/

/**

@defgroup tools Standalone utility applications

Some utility applications are listed here. 

The standard compilation procedure (<tt>./configure;make</tt>) will compile

them, as well. 

*/